OR-Transformer: Scaling Real-Time Decision-Making to 1,000 Items

Modern supply chain operations can require coordinating replenishment across thousands of heterogeneous items under correlated stochastic demand, heterogeneous lead times, and shared fixed ordering costs, yielding observation spaces exceeding $10^4$ dimensions. At this scale, rolling-horizon stochastic mixed-integer linear programs (MILPs) become prohibitively slow, while standard reinforcement learning (RL) methods face increasingly challenging credit assignment in high-dimensional action spaces. We introduce OR-Transformer, a deep reinforcement learning framework for joint replenishment under stochastic demand, with an item-permutation-equivariant Transformer architecture and pathwise-gradient training through the inventory dynamics. Across problem sizes up to 1,024 inventory items, OR-Transformer increasingly outperforms learning-based and rolling-horizon MILP baselines as scale grows. It also reduces online decision-making time by over 4 million times relative to MILP solvers, enabling real-time, large-scale deep RL in supply chain operations.

Resource-Adaptive Primal-Dual Learning for One-Warehouse Multi-Store Systems with Censored Demand

The one-warehouse multi-store (OWMS) system is a fundamental inventory network in which a nonreplenishable warehouse allocates shared stock across multiple stores over time. Existing OWMS learning policies are built around a fixed target calibrated to the initial average resource rate, but such a fixed-target architecture cannot re-center after realized sales change the remaining resource available per future period. We develop Resource-Adaptive Primal-Dual Learning, a new learning framework that tracks the primal-dual resolving path with censored demand as the remaining-resource state evolves. In each period, the current resource rate indexes the target store allocations and dual variable, while censored sales provide gradient estimates for updating both. The analysis combines expected-sales geometry with a moving-target argument to yield logarithmic expected regret, improving on the state-of-the-art square-root-order guarantees of existing OWMS learning policies. The underlying design and analytical ideas may inform other online learning problems with depleting shared resources. Numerical experiments further demonstrate good finite-horizon performance of a practical variant across different horizon lengths and inventory regimes.

Contextual Deconvolution for Variance-Stable Demand Sensing: Kernel-Modulated Operators in Promotional Retail

Machine learning demand forecasts optimize statistical accuracy yet leave excess operational volatility that inflates safety stock and amplifies the Bullwhip effect. We introduce \textbf{Contextual Deconvolution} (CD), a two-stage estimator that reframes demand sensing as a convex decomposition: a kernel-modulated banded operator separates transient promotion-driven shocks from a smooth structural baseline, and hierarchical partial pooling enables catalog-scale deployment without per-SKU training. The operator is data-derived, not imposed---it reduces to the identity wherever the promotional response is impulsive (most of M5, all of Favorita) and contributes only where genuine multi-day carryover exists, so the gains rest on the structural decomposition itself. Evaluating strictly out-of-sample on 30,490 M5 SKUs and 2,845 Favorita items, with calendar-aware baselines given CD's identical future calendar, we anchor the contribution on a full inventory-cost accounting: CD lowers safety stock, holding cost, and order variance but under-provisions event spikes, reducing total cost only when holding costs exceed $\sim$20\% of stockout costs (95\% CI $[17\%,25\%]$); otherwise it is an operational-stability and inventory-capital layer, not an expected-cost minimizer. Its accuracy contribution is reliability rather than central tendency: across eleven baselines, CD attains the lowest cross-sectional dispersion of per-SKU error and mis-forecasts by more than 200\% on 0.8\% of SKUs versus 9.9--20.6\% for every baseline, ranking first on both in all four M5 draws. Because the Variance Ratio and std-based safety stock are minimized by any sufficiently smooth forecast, we treat them as diagnostics, not objectives. A supporting analysis shows the learned demand operators are non-normal, yet CD's compact parametric kernel matches their operational performance interpretably.

UC-Search: Risk-Aware Test-Time Search for Delayed Constrained Time-Series Control

Time-series models are usually scored as forecasters, yet deployed systems often require delayed decisions under uncertainty and hard feasibility constraints. UC-Search is a model-agnostic test-time wrapper: a backbone emits forecasts or action scores, a feasibility automaton rolls candidate paths forward, and bounded search returns the first action of a risk-adjusted feasible trajectory. We instantiate UC-Beam and a UCT-style UC-MCTS diagnostic, using epistemic, aleatoric, and propagated uncertainty mainly as path-risk terms. A myopic-collapse/separation theorem states when search reduces to one-step risk-greedy and when delayed feasible-set coupling can create non-myopic value. Primary evidence comes from a predeclared public $9$-family, $33$-series delayed-control suite with six held-out starts per series: UC-Pareto is positive versus validation-selected CEM, MPPI, and risk-aware random at the normalized threshold ($+3.1675/+2.3328/+2.5038$), and remains positive in a compute-matched audit ($+2.8466/+2.7418/+2.7429$). ETT/LTSF delayed-inventory validation supports the same compute-frontier claim. A 48-series raw M4 standard periodic-review lost-sales inventory audit is positive versus the strongest classic base-stock control ($+13556.7547$), CEM ($+64900.2207$), and risk-random ($+52881.6042$), while MPPI remains family-mixed. FI-2010, official-forecast adapters, SB3/FQI controls, direction/capacity/intervention checks, and synthetic mechanism tests are reported as boundary or mechanism evidence rather than broad dominance claims.

Optimal Hidden-Target Learning for Online Inventory Optimization on General Convex Sets

Online inventory optimization (OIO) is online convex optimization with physical memory: inventory carryover makes the feasible action set depend on the past. A natural principle, used in stochastic inventory learning and recently in OIO under a single linear capacity constraint, is to maintain a hidden target chosen by an online learner and implement its projection onto the currently feasible order-up-to set. We prove that this simple principle is optimal for OIO on arbitrary bounded convex capacity sets. With online gradient descent as the base learner, the method improves the best known regret guarantee for OIO on general convex sets from inverse to inverse-square-root dependence on the common-demand probability, and we prove a matching lower bound. The same principle gives the first polylogarithmic regret guarantee for strongly convex losses and the first dynamic regret guarantee adapting to Euclidean path variation on general convex capacity sets. The analysis introduces a norm alignment principle: the right state variable is the distance from the hidden target to the feasible set, measured in the same norm as the projection. Under norm alignment, this distance evolves pathwise as a scalar queue, with target movement as arrival and common demand as service. This reduction to one-dimensional queue control resolves the state dependence and extends the guarantees to general convex capacity sets, beyond the reach of prior productwise approaches. Experiments on synthetic and real-world inventory data corroborate the theory.

Learning to replenish: A hybrid deep reinforcement learning for dynamic inventory management in the pharmaceutical supply chains

Pharmaceutical supply chains (PSCs) struggle with inventory management (IM) due to unpredictable demand patterns and variable lead times associated with restocking. This complexity is further compounded by the finite shelf lives of pharmaceutical products, which necessitate a delicate balance between adequate stock and minimal waste. These intertwined factors create a complex optimization problem that requires sophisticated inventory strategies to ensure both product availability and PSC efficiency. This study aims to develop an optimal inventory replenishment policy for pharmaceutical products that can handle the stochasticity arising from uncertain demand and variable PSC conditions. The objective is to maximize the profitability of the PSC while maintaining a high patient service level. We formulate the problem as a Markov decision process and propose a deep reinforcement learning (DRL) approach, specifically, a hybrid asynchronous advantage actor critic distributed proximal policy optimization (A3C DPPO)algorithm. The A3C DPPO algorithm is tailored to handle the continuous action space inherent in IM. The numerical results demonstrate that the proposed algorithm adaptively updates the inventory replenishment strategy under dynamic scenarios, resulting in lower inventory costs compared to various benchmarks. We also conduct numerical validation using real-world pharmaceutical inventory data to confirm the practical feasibility of the proposed algorithm.